TORQUE HYSTERESIS CONTROLLER FOR BRUSHLESS DC MOTOR DRIVES.
Power and Energy Conversion Symposium (PECS 2012)
Melaka, Malaysia
17 Dec 2012
TORQUE HYSTERESIS CONTROLLER FOR BRUSHLESS DC MOTOR
DRIVES
Ahmad Faiz Noor Azam , Mustafa Manap, Auzani Jidin, Norhazilina Bahari, Hatta Jopri,
Abdul Rahim bin Abdullah
Department Of Power Electronics Drives,
Faculty of Electrical Engineering,
Universiti Teknikal Malaysia Melaka (UTeM)
Hang Tuah Jaya, 76100 Durian Tunggal, Malacca, Malaysia
that creates a rotating magnetic field. The rotor position
needs to be determined so that excitation of the stator
field always leads the permanent magnet field to produce
torque. The commutation instants are determined by the
rotor position and the position of the rotor is detected
either by position sensors or by sensorless techniques.
The signals from Hall Effect sensors that usually used in
BLDC motor need to decode to determine the shaft and
energize the appropriate stator windings.
BLDC motors are available in many different power
ratings, which vary from very small motor as used in hard
disk drives to large motor used in electric vehicles.
BLDC motor attracts much interest due to its high
efficiency, high power factor, high power density,
compactness, high torque, simple control and lower
maintenance. The power circuit components that are
required to convert from alternating current to direct
current provide the basis for variable-speed drive, making
BLDC motors well-suited for applications that require
speed control over a wide operating range. The
permanent magnets used in BLDC motor helps to keep
the inertia low. The BLDC motor generates less heat
because there is no current flow in the rotor thus allowing
efficient heat dissipation from the BLDC motor’s wound
stator to the outer metallic housing.
The simulation of a torque hysteresis controller for
BLDC motor drive system is developed using
‘Matlab/Simulink’. The simulation circuit includes all
realistic components of the drive system. The concept of
torque hysteresis controller is basically similar to
hysteresis current controller because the torque is
proportional to the current. A comparative study
associated with hysteresis and PWM techniques in
current controllers has been made. By comparing these
techniques, hysteresis current controller is chosen
considering its easy implementation, quick response,
maximum current limit and insensitive to load parameter
variations.
Abstract— The presence of the commutator and brushes in
a dc machine enforce severe limitations on its voltage and
current ratings, means that the output power capability of a
dc machine is restricted. The mechanical commutator in a
dc machine limits its high speed capabilities. Both the
brushes and commutator of a dc machine require regular
maintenance. In addition, dc machines are prone to
sparking and cannot be normally used in explosive
atmosphere. The dust produced by brush wear, makes the
dc machine undesirable for use in certain industries like the
semiconductor or food industries. Thus, to overcome this
problem BLDC machine is proposed due to its advantages
over the conventional dc machine. The torque hysteresis
controller is presented as the technique chosen to control the
phase current and torque of the BLDC machine. This
method used to replace the voltage control in BLDC
machine. Voltage control is conventional methods used but
have a very high current overshoot, by using torque
hysteresis controller it will provide current protection which
is the value of current and torque will stay within certain
limits around with reference value.
Keywords-components; Brushless DC motor; hall effect;
torque hysteresis controller
I.
INTRODUCTION
Conventional dc motors are highly efficient and their
characteristics make it reliable for use in many
applications. However, the only drawback is that it uses
commutator and brushes that require frequent
maintenance and cannot be performed at dirty and
explosive environment and at very high speed operating
conditions [1]. When the functions of commutator and
brushes were replaced by solid-state switches,
maintenance-free motor were developed. These types of
motors are now known as brushless dc motors. Brushless
dc (BLDC) motors are in fact a type of permanent magnet
synchronous motors. It is driven by dc voltage and the
current commutation is done by solid state switches.
BLDC motor implements the basic operating principles
of DC motor operation but with a difference by placing
the permanent magnet in the rotor and coils in the stator.
The coil windings are electrically separate from each
other which allow it to be turn on and off in a sequence
II.
CONSTRUCTION OF BLDC MOTOR
BLDC motor is a synchronous type of motor which the
magnetic field generated by stator and rotor rotates at the
69
Power and Energy Conversion Symposium (PECS 2012)
Melaka, Malaysia
17 Dec 2012
same frequency, hence eliminating the slip which is
normally seen in induction machine. BLDC motor has
two primary pats which is rotor (rotating part), stator
(stationary part) and permanent magnet of the rotor.
There are two basic rotor designs which is inner rotor and
the other one is outer rotor.
For the inner rotor design, the stator winding surround
the rotor and are fixed at motor housing. The advantages
of the design are the ability to dissipate heat thus directly
impacts its ability to generate torque and its lower inertia.
For the outer rotor design, the winding are located in the
core of the motor. The rotor magnets surround the stator
windings and acts as an insulator, reducing the rate of
heat dissipation from the motor. This design operates at
lower duty cycles or at lower rated current. The
advantage of this design is relatively low cogging torque.
The winding slots are built into the stator and changing
magnetic field is provided by the current polarity changes
in the slot windings. The change of current polarity must
be in accordance to the rotor magnetic field, which
requires the position of the rotor. Hall effect sensors are
fixed on the stator to provide this information. Solid state
switches are used for current commutation which
eliminates the need of brushes.
There are two types of back-emf that a BLCD motor
can generate which are trapezoidal and sinusoidal
waveforms.[2] The back-emf is determined by the
manner in which windings are placed in the stator, either
concentrated or distributed windings. Concentrated
windings produce a trapezoidal back-emf while
distributed windings result in a sinusoidal back-emf.
For the permanent magnet rotor, there are also two
designs which are practiced. The first design place the
permanent magnet onto the surface of the rotor, see figure
1. By placing the magnet onto the rotor reduces the
manufacturing time but during high speed condition there
is possibilities that the magnet might fly off the rotor. For
the other design the magnets are inserted beneath the
surface of the rotor, see Figure 2. This practice requires
additional machining of the rotor to create the slots for
the magnets which in the end increased the
manufacturing time and cost. However, the advantage is
that the motor can be operated at very high speed
conditions without the danger of magnet failure.
Stator
Stator Pole
Rotor
Copper coil
Figure 2. BLDC motor cross section for inner mounted PM’s
The three phase BLDC motor is operated in a twophases-on fashion which is mean the two phases that
produce the highest torque are energized while the third
phase is off, see Figure 3. The two phases are energized
depends on the rotor position. The signals from the
position sensors produce a three digit number that
changes every 60 degree (electrical degrees). Current
commutation is done by a six-step inverter.
Figure 3. BLDC motor cross section and phase energizing sequence.
The power electronic converter is necessary to operate
the BLDC machine. The converter is three phases DC to
AC converter and it consists of six solid state
semiconductor switches. Mosfets and IGBT are the most
common types of switches used. In lower power
application, mosfets are preferred over IGBT. The power
ap
electronic inverter must be capable of applying positive,
el
negative and zero voltage across the motor phase
terminals. Each drive phase consists of one motor
terminal driven high, one motor terminal driven low, and
one motor terminal floating [2].
Magnets on the rotor
Stator
Stator Pole
Rotor
Magnets
inside the
rotor
Cooper Coil
Figure 1. BLDC motor cross section for surface mounted PM’s
70
Power and Energy Conversion Symposium (PECS 2012)
Melaka, Malaysia
17 Dec 2012
Figure 4. Three-Phase DC to AC inverter.
III.
It should be noted that the production of torque is the
summation of the torque produced for each phase;
MODELLING OF BLDC MACHINES
ܶ ሺݐሻ ൌ
Mathematical modeling of a BLDC motor can be
derived similar to DC machines where there are two
equivalent circuits, i.e electrical and mechanical
equations. Figure 5 shows the basic blocks of BLDC
motor that contains three phase stator circuit and
mechanical part. The main difference compare to DC
machines is the construction of the machine where it has
three phase windings at the stator (with n number of
poles) and the rotor equipped with permanent magnet
which is positioned at the center of the motor by the
bearing. The rotor is not electrically connected to the
stator thus preventing arcing phenomena which cause
carbon to be produce hence making insulation failure.
ܶǡ ሺݐሻ ൌ ݅ ሺݐሻǤ ݇ ்ǡ ሺߐሻ
݁ ሺݐሻ ൌ ݇௩ǡ ሺߐሻǤ ߱ (t)
where,
ௗ௧
ሺݐሻ ݁ ሺt)
(3)
(4)
(5)
where, the torque factor kT,k(ϴ) can be assumed
equivalent to the back-emf voltage factor kV,k(ϴ). The
angular velocity (ωe) is multiplication of rotor angular
velocity and number of poles of the machine, i.e. ω x
number of poles. For trapezoidal operated in BLDC
motor, the kT,k(ϴ) and kV,k(ϴ) are not constant as opposed
to the constant field operated in brushes DC motor. Given
the rotor position (ϴ), these factors can be simply
obtained using piece-wise normalized trapezoidal
function as illustrated in Fig. 5.
From Fig. 5, it can be noticed that each phase winding
is conducted in sequence for 1200 per one cycle of period
to carry either positive or negative constant current. The
conduction of each phase winding is determined by the
rotor position where the position can be known from hall
effect sensors that provides three digitized output. The
generation of three digitized outputs (i.e. H1,H2 and H3)
from the sensor according to the rotor position can be
also described in Fig. 5.
For simplification, the electrical model is expressed for
one phase of stator winding, e.g. phase k (k = a,b or c) as
given by (1).
ௗೖ
ܶǡ ሺݐሻ
The productions of torque and back-emf voltage for each
phase are calculated as;
Figure 5. Three phase Brushless DC machine equivalent circuit and
mechanical model.
ݒ ሺݐሻ ൌ ݅ ୩ ୩
ୀǡୟ୬ୢ
(1)
vkn(t)•
= instantaneous of k-phase voltage
ik (t)
= instantaneous of k-phase current
ek (t)
= instantaneous of k-phase back-emf voltage
Rk
= k-phase resistance
Lk
= k-phase inductance
On the other hand, the mechanical model of BLDC
machine actually represents the production of torque as
given by (2).
ܶ ሺݐሻ ൌ
where,
݀߱ሺݐሻ
߱ሺݐሻ ܶ ሺݐሻ
݀ݐ
ω(t)•
= rotor angular velocity
B•
= viscous friction
J
= moment of inertia
TL
= load torque
(2)
Figure 6. Three phase Brushless DC machine equivalent circuit and
mechanical model.
71
Power and Energy Conversion Symposium (PECS 2012)
Melaka, Malaysia
17 Dec 2012
IV.
TORQUE HYSTERESIS CONTROLLER
Each phase current is controlled using a 2-level
hysteresis comparator, which is responsible to produce
appropriate switching status to be fed into the inverter,
either to increase or decrease the phase current such that
its error (or current ripple) is restricted within the
hysteresis band (HB). In such a way, the reference current
for each phase will have the same pattern waveform with
the respective decoded signals. .
Hysteresis control is one of the simplest closed-loop
control schemes. In hysteresis control, the value of the
controlled variable is forced to stay within certain limits
around a reference value. As an example, to control
motor speed, the motor is turned off if the speed reaches a
certain level above the reference speed and turned back
on when the speed falls below a certain level below the
reference speed. Nevertheless, due to lack of coordination
among individual hysteresis controller of three phase,
very high switching frequency at lower modulation index
may happen[3].
The drawbacks of the hysteresis band control
technique are the high and uncontrolled switching
frequencies when a narrow hysteresis band is used and
large ripples when the hysteresis band is wider [4]. The
uncertain switching frequency make filtering of acoustic
and electromagnetic noise become difficult [5]. The
switching method used here is the soft chopping method
which is only the upper switch is turned on and off while
the lower switch is left on. This method produces less
torque ripple and less switching losses than the hard
chopping method. Only torque control and speed control
is implemented here. The reason is that if position control
were to be implemented in the same way as the torque
and the position control, it would only be possible by
constantly reversing the rotor speed so that the rotor angle
would stay within the hysteresis band.
It is desirable to provide current limitation and fast
torque dynamic control for many electric drive
applications. A simple method that can offer these
requirements is the use of torque hysteresis controller
(THC) technique. Figure 6 shows the structure of torque
hysteresis controller for BLDC motor
The control of torque can be established by controlling
the three-phase current at its reference such that it will
satisfy the equations (3) and (4). As shown by Fig. 6, the
motor currents need to be controlled satisfying to their
references (ia*, ib* and ic*). The generations of reference
currents are based on the torque demand (i.e. I ref = Te,ref x
G1) and decoded signals (H1’, H2’ and H3’) which are
derived from the Hall Effect signals (H1, H2 and H3) as
given in Table 1.
2-level
Hysteresis
Comparators
ia* +
Te,ref
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
-1
+1
0
-1
+1
+1
0
Iref
ib*
X
+
1
0
+
-
1
0
Sa
Current
Source
Inverter
(CSI)
Sb
Sc
ic ib ia
Decoded signals
(H1’, H2’, H3’)
Deco
Decoder
Hall Effect signals (H1, H2, H3)
BLDC
Figure 7. Structure of Torque Hysteresis Controller (THC) drive for
BLDC motor.
V.
EXPERIMENTAL RESULTS
The brushless DC motor drive system has been
realized and tested in laboratory. The experimental setup
consists of hysteresis current control, accurate speed and
position information, a secure three phase DC/AC
inverter, digital signal processor and an appropriately size
BLDC machine and load. The control and motor
parameters values used for this experiment are shown in
Table 2.
TABLE 2
Decoded Signals
H 1’
H 2’
H 3’
0
0
-1
-1
+1
0
0
0
G1
[A/Nm]
ic*
TABLE 1 Derivation of Decoded Signals based on Hall
Effect Signals
Hall Eff. Signals
H1
H2
H3
1
0
-
+ VDC -
0
+1
0
+1
0
-1
-1
0
Control and Motor Parameters Values
Control System
Hysteresis band
Sampling time
BLDC Motor
Stator resistance
Stator inductance
Flux linkage established by magnets
Torque constant
Moment of inertia
0.2 "
8.5 mH
0.175 V.s
1.4 Nm/A
0.04 Kg.m2
Friction factor
Pole pairs
0.005 Nms
4
0.2 A
50 !s
Figure 8 shows the current waveforms in THC
obtained for the experiment. It can be observed that the
motor current for each phase is controlled at its reference.
By applying the hysteresis controller, the current error
ripple is restricted within the predefined band gap. The
current references are determined by the torque demand
and decoded signals.
72
Power and Energy Conversion Symposium (PECS 2012)
Melaka, Malaysia
17 Dec 2012
REFERENCES
[1]
[2]
[3]
[4]
[5]
Figure 8. Motor currents are controlled such that it follows their
references which were generated based on the hall effect signals
[6]
Figure 9 shows the speed and current output
waveforms of the motor. It can be observed as the speed
decreases (during motor braking) the frequency of the
current waveforms decreases and as the speed increase
(during motor acceleration) the frequency of the current
waveforms increases. Another phenomenon that can be
observed is the phase sequence of the current. If the speed
of the motor is above 0, the phases of the current are as
follows, (cyan, blue and green) while during negative
speed, the phases of the current are as follows (green,
blue and cyan)
[7]
[8]
[9]
[10]
Figure 9. Experimental results showing output waveforms of speed and
currents.
VI.
CONCLUSIONS
This paper has presented the modelling and
experimental result of torque hysteresis controller for
BLDC motor. Torque hysteresis controller has been
applied to a BLDC drive and the results shows that the
current ripple stays within the hysteresis band as defined
by the controller.
ACKNOWLEDGMENT
The authors would like to thank the Universiti Teknikal
Malaysia Melaka (UTeM) for providing the grant for this
research.
73
Lefley, P., L. Petkovska, and G. Cvetkovski. Optimization of
the design parameters of an asymmetric brushless DC motor
for cogging torque minimization in Power Electronics and
Applications (EPE 2011), Proceeding of the 2011-14th
European Conference on 2011.
Hendershot, J.R and T. Miller. Design of Brushless PermanentMagnet Motors. Oxford: Magna Physics Publications &
Oxford Science Publication, 1994.
Ching-Tsai, P. and C. Ting-Yu, An improved hysteresis current
controller for reducing switching frequency. Power Electronics,
IEEE Transactions on, 1994. 9(1): p. 97-104.
KS Low M.F Rahman and K.W Lim. Approaches to the
Control of Torque and Current in Brushless Dc Drive,2002.
Texas Instruments Incorporated. DSP Solutions for BLDC
Motors,1997.
Mayer, J.S. and O. Wasynczuk, Analysis and modelling of a
single-phase brushless DC motor drive system. Energy
Conversion, IEEE Transactions on, 1989. 4(3): p. 473-479.
P.C Sen. Principles of Electric Machine and Power Electronics,
John Wiley,1997. .
Hart, Daniel W. Introduction of Power Electronic, Prentice
hall,2002.
El-Shakawi, A Mohamed. Fundamental of Motor Drives,
Books/Cole Publishing Company,2000.
Anand Sathyan. Digital PWM Control of Brushless Dc Motor
drives, Dec 2008.
Melaka, Malaysia
17 Dec 2012
TORQUE HYSTERESIS CONTROLLER FOR BRUSHLESS DC MOTOR
DRIVES
Ahmad Faiz Noor Azam , Mustafa Manap, Auzani Jidin, Norhazilina Bahari, Hatta Jopri,
Abdul Rahim bin Abdullah
Department Of Power Electronics Drives,
Faculty of Electrical Engineering,
Universiti Teknikal Malaysia Melaka (UTeM)
Hang Tuah Jaya, 76100 Durian Tunggal, Malacca, Malaysia
that creates a rotating magnetic field. The rotor position
needs to be determined so that excitation of the stator
field always leads the permanent magnet field to produce
torque. The commutation instants are determined by the
rotor position and the position of the rotor is detected
either by position sensors or by sensorless techniques.
The signals from Hall Effect sensors that usually used in
BLDC motor need to decode to determine the shaft and
energize the appropriate stator windings.
BLDC motors are available in many different power
ratings, which vary from very small motor as used in hard
disk drives to large motor used in electric vehicles.
BLDC motor attracts much interest due to its high
efficiency, high power factor, high power density,
compactness, high torque, simple control and lower
maintenance. The power circuit components that are
required to convert from alternating current to direct
current provide the basis for variable-speed drive, making
BLDC motors well-suited for applications that require
speed control over a wide operating range. The
permanent magnets used in BLDC motor helps to keep
the inertia low. The BLDC motor generates less heat
because there is no current flow in the rotor thus allowing
efficient heat dissipation from the BLDC motor’s wound
stator to the outer metallic housing.
The simulation of a torque hysteresis controller for
BLDC motor drive system is developed using
‘Matlab/Simulink’. The simulation circuit includes all
realistic components of the drive system. The concept of
torque hysteresis controller is basically similar to
hysteresis current controller because the torque is
proportional to the current. A comparative study
associated with hysteresis and PWM techniques in
current controllers has been made. By comparing these
techniques, hysteresis current controller is chosen
considering its easy implementation, quick response,
maximum current limit and insensitive to load parameter
variations.
Abstract— The presence of the commutator and brushes in
a dc machine enforce severe limitations on its voltage and
current ratings, means that the output power capability of a
dc machine is restricted. The mechanical commutator in a
dc machine limits its high speed capabilities. Both the
brushes and commutator of a dc machine require regular
maintenance. In addition, dc machines are prone to
sparking and cannot be normally used in explosive
atmosphere. The dust produced by brush wear, makes the
dc machine undesirable for use in certain industries like the
semiconductor or food industries. Thus, to overcome this
problem BLDC machine is proposed due to its advantages
over the conventional dc machine. The torque hysteresis
controller is presented as the technique chosen to control the
phase current and torque of the BLDC machine. This
method used to replace the voltage control in BLDC
machine. Voltage control is conventional methods used but
have a very high current overshoot, by using torque
hysteresis controller it will provide current protection which
is the value of current and torque will stay within certain
limits around with reference value.
Keywords-components; Brushless DC motor; hall effect;
torque hysteresis controller
I.
INTRODUCTION
Conventional dc motors are highly efficient and their
characteristics make it reliable for use in many
applications. However, the only drawback is that it uses
commutator and brushes that require frequent
maintenance and cannot be performed at dirty and
explosive environment and at very high speed operating
conditions [1]. When the functions of commutator and
brushes were replaced by solid-state switches,
maintenance-free motor were developed. These types of
motors are now known as brushless dc motors. Brushless
dc (BLDC) motors are in fact a type of permanent magnet
synchronous motors. It is driven by dc voltage and the
current commutation is done by solid state switches.
BLDC motor implements the basic operating principles
of DC motor operation but with a difference by placing
the permanent magnet in the rotor and coils in the stator.
The coil windings are electrically separate from each
other which allow it to be turn on and off in a sequence
II.
CONSTRUCTION OF BLDC MOTOR
BLDC motor is a synchronous type of motor which the
magnetic field generated by stator and rotor rotates at the
69
Power and Energy Conversion Symposium (PECS 2012)
Melaka, Malaysia
17 Dec 2012
same frequency, hence eliminating the slip which is
normally seen in induction machine. BLDC motor has
two primary pats which is rotor (rotating part), stator
(stationary part) and permanent magnet of the rotor.
There are two basic rotor designs which is inner rotor and
the other one is outer rotor.
For the inner rotor design, the stator winding surround
the rotor and are fixed at motor housing. The advantages
of the design are the ability to dissipate heat thus directly
impacts its ability to generate torque and its lower inertia.
For the outer rotor design, the winding are located in the
core of the motor. The rotor magnets surround the stator
windings and acts as an insulator, reducing the rate of
heat dissipation from the motor. This design operates at
lower duty cycles or at lower rated current. The
advantage of this design is relatively low cogging torque.
The winding slots are built into the stator and changing
magnetic field is provided by the current polarity changes
in the slot windings. The change of current polarity must
be in accordance to the rotor magnetic field, which
requires the position of the rotor. Hall effect sensors are
fixed on the stator to provide this information. Solid state
switches are used for current commutation which
eliminates the need of brushes.
There are two types of back-emf that a BLCD motor
can generate which are trapezoidal and sinusoidal
waveforms.[2] The back-emf is determined by the
manner in which windings are placed in the stator, either
concentrated or distributed windings. Concentrated
windings produce a trapezoidal back-emf while
distributed windings result in a sinusoidal back-emf.
For the permanent magnet rotor, there are also two
designs which are practiced. The first design place the
permanent magnet onto the surface of the rotor, see figure
1. By placing the magnet onto the rotor reduces the
manufacturing time but during high speed condition there
is possibilities that the magnet might fly off the rotor. For
the other design the magnets are inserted beneath the
surface of the rotor, see Figure 2. This practice requires
additional machining of the rotor to create the slots for
the magnets which in the end increased the
manufacturing time and cost. However, the advantage is
that the motor can be operated at very high speed
conditions without the danger of magnet failure.
Stator
Stator Pole
Rotor
Copper coil
Figure 2. BLDC motor cross section for inner mounted PM’s
The three phase BLDC motor is operated in a twophases-on fashion which is mean the two phases that
produce the highest torque are energized while the third
phase is off, see Figure 3. The two phases are energized
depends on the rotor position. The signals from the
position sensors produce a three digit number that
changes every 60 degree (electrical degrees). Current
commutation is done by a six-step inverter.
Figure 3. BLDC motor cross section and phase energizing sequence.
The power electronic converter is necessary to operate
the BLDC machine. The converter is three phases DC to
AC converter and it consists of six solid state
semiconductor switches. Mosfets and IGBT are the most
common types of switches used. In lower power
application, mosfets are preferred over IGBT. The power
ap
electronic inverter must be capable of applying positive,
el
negative and zero voltage across the motor phase
terminals. Each drive phase consists of one motor
terminal driven high, one motor terminal driven low, and
one motor terminal floating [2].
Magnets on the rotor
Stator
Stator Pole
Rotor
Magnets
inside the
rotor
Cooper Coil
Figure 1. BLDC motor cross section for surface mounted PM’s
70
Power and Energy Conversion Symposium (PECS 2012)
Melaka, Malaysia
17 Dec 2012
Figure 4. Three-Phase DC to AC inverter.
III.
It should be noted that the production of torque is the
summation of the torque produced for each phase;
MODELLING OF BLDC MACHINES
ܶ ሺݐሻ ൌ
Mathematical modeling of a BLDC motor can be
derived similar to DC machines where there are two
equivalent circuits, i.e electrical and mechanical
equations. Figure 5 shows the basic blocks of BLDC
motor that contains three phase stator circuit and
mechanical part. The main difference compare to DC
machines is the construction of the machine where it has
three phase windings at the stator (with n number of
poles) and the rotor equipped with permanent magnet
which is positioned at the center of the motor by the
bearing. The rotor is not electrically connected to the
stator thus preventing arcing phenomena which cause
carbon to be produce hence making insulation failure.
ܶǡ ሺݐሻ ൌ ݅ ሺݐሻǤ ݇ ்ǡ ሺߐሻ
݁ ሺݐሻ ൌ ݇௩ǡ ሺߐሻǤ ߱ (t)
where,
ௗ௧
ሺݐሻ ݁ ሺt)
(3)
(4)
(5)
where, the torque factor kT,k(ϴ) can be assumed
equivalent to the back-emf voltage factor kV,k(ϴ). The
angular velocity (ωe) is multiplication of rotor angular
velocity and number of poles of the machine, i.e. ω x
number of poles. For trapezoidal operated in BLDC
motor, the kT,k(ϴ) and kV,k(ϴ) are not constant as opposed
to the constant field operated in brushes DC motor. Given
the rotor position (ϴ), these factors can be simply
obtained using piece-wise normalized trapezoidal
function as illustrated in Fig. 5.
From Fig. 5, it can be noticed that each phase winding
is conducted in sequence for 1200 per one cycle of period
to carry either positive or negative constant current. The
conduction of each phase winding is determined by the
rotor position where the position can be known from hall
effect sensors that provides three digitized output. The
generation of three digitized outputs (i.e. H1,H2 and H3)
from the sensor according to the rotor position can be
also described in Fig. 5.
For simplification, the electrical model is expressed for
one phase of stator winding, e.g. phase k (k = a,b or c) as
given by (1).
ௗೖ
ܶǡ ሺݐሻ
The productions of torque and back-emf voltage for each
phase are calculated as;
Figure 5. Three phase Brushless DC machine equivalent circuit and
mechanical model.
ݒ ሺݐሻ ൌ ݅ ୩ ୩
ୀǡୟ୬ୢ
(1)
vkn(t)•
= instantaneous of k-phase voltage
ik (t)
= instantaneous of k-phase current
ek (t)
= instantaneous of k-phase back-emf voltage
Rk
= k-phase resistance
Lk
= k-phase inductance
On the other hand, the mechanical model of BLDC
machine actually represents the production of torque as
given by (2).
ܶ ሺݐሻ ൌ
where,
݀߱ሺݐሻ
߱ሺݐሻ ܶ ሺݐሻ
݀ݐ
ω(t)•
= rotor angular velocity
B•
= viscous friction
J
= moment of inertia
TL
= load torque
(2)
Figure 6. Three phase Brushless DC machine equivalent circuit and
mechanical model.
71
Power and Energy Conversion Symposium (PECS 2012)
Melaka, Malaysia
17 Dec 2012
IV.
TORQUE HYSTERESIS CONTROLLER
Each phase current is controlled using a 2-level
hysteresis comparator, which is responsible to produce
appropriate switching status to be fed into the inverter,
either to increase or decrease the phase current such that
its error (or current ripple) is restricted within the
hysteresis band (HB). In such a way, the reference current
for each phase will have the same pattern waveform with
the respective decoded signals. .
Hysteresis control is one of the simplest closed-loop
control schemes. In hysteresis control, the value of the
controlled variable is forced to stay within certain limits
around a reference value. As an example, to control
motor speed, the motor is turned off if the speed reaches a
certain level above the reference speed and turned back
on when the speed falls below a certain level below the
reference speed. Nevertheless, due to lack of coordination
among individual hysteresis controller of three phase,
very high switching frequency at lower modulation index
may happen[3].
The drawbacks of the hysteresis band control
technique are the high and uncontrolled switching
frequencies when a narrow hysteresis band is used and
large ripples when the hysteresis band is wider [4]. The
uncertain switching frequency make filtering of acoustic
and electromagnetic noise become difficult [5]. The
switching method used here is the soft chopping method
which is only the upper switch is turned on and off while
the lower switch is left on. This method produces less
torque ripple and less switching losses than the hard
chopping method. Only torque control and speed control
is implemented here. The reason is that if position control
were to be implemented in the same way as the torque
and the position control, it would only be possible by
constantly reversing the rotor speed so that the rotor angle
would stay within the hysteresis band.
It is desirable to provide current limitation and fast
torque dynamic control for many electric drive
applications. A simple method that can offer these
requirements is the use of torque hysteresis controller
(THC) technique. Figure 6 shows the structure of torque
hysteresis controller for BLDC motor
The control of torque can be established by controlling
the three-phase current at its reference such that it will
satisfy the equations (3) and (4). As shown by Fig. 6, the
motor currents need to be controlled satisfying to their
references (ia*, ib* and ic*). The generations of reference
currents are based on the torque demand (i.e. I ref = Te,ref x
G1) and decoded signals (H1’, H2’ and H3’) which are
derived from the Hall Effect signals (H1, H2 and H3) as
given in Table 1.
2-level
Hysteresis
Comparators
ia* +
Te,ref
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
-1
+1
0
-1
+1
+1
0
Iref
ib*
X
+
1
0
+
-
1
0
Sa
Current
Source
Inverter
(CSI)
Sb
Sc
ic ib ia
Decoded signals
(H1’, H2’, H3’)
Deco
Decoder
Hall Effect signals (H1, H2, H3)
BLDC
Figure 7. Structure of Torque Hysteresis Controller (THC) drive for
BLDC motor.
V.
EXPERIMENTAL RESULTS
The brushless DC motor drive system has been
realized and tested in laboratory. The experimental setup
consists of hysteresis current control, accurate speed and
position information, a secure three phase DC/AC
inverter, digital signal processor and an appropriately size
BLDC machine and load. The control and motor
parameters values used for this experiment are shown in
Table 2.
TABLE 2
Decoded Signals
H 1’
H 2’
H 3’
0
0
-1
-1
+1
0
0
0
G1
[A/Nm]
ic*
TABLE 1 Derivation of Decoded Signals based on Hall
Effect Signals
Hall Eff. Signals
H1
H2
H3
1
0
-
+ VDC -
0
+1
0
+1
0
-1
-1
0
Control and Motor Parameters Values
Control System
Hysteresis band
Sampling time
BLDC Motor
Stator resistance
Stator inductance
Flux linkage established by magnets
Torque constant
Moment of inertia
0.2 "
8.5 mH
0.175 V.s
1.4 Nm/A
0.04 Kg.m2
Friction factor
Pole pairs
0.005 Nms
4
0.2 A
50 !s
Figure 8 shows the current waveforms in THC
obtained for the experiment. It can be observed that the
motor current for each phase is controlled at its reference.
By applying the hysteresis controller, the current error
ripple is restricted within the predefined band gap. The
current references are determined by the torque demand
and decoded signals.
72
Power and Energy Conversion Symposium (PECS 2012)
Melaka, Malaysia
17 Dec 2012
REFERENCES
[1]
[2]
[3]
[4]
[5]
Figure 8. Motor currents are controlled such that it follows their
references which were generated based on the hall effect signals
[6]
Figure 9 shows the speed and current output
waveforms of the motor. It can be observed as the speed
decreases (during motor braking) the frequency of the
current waveforms decreases and as the speed increase
(during motor acceleration) the frequency of the current
waveforms increases. Another phenomenon that can be
observed is the phase sequence of the current. If the speed
of the motor is above 0, the phases of the current are as
follows, (cyan, blue and green) while during negative
speed, the phases of the current are as follows (green,
blue and cyan)
[7]
[8]
[9]
[10]
Figure 9. Experimental results showing output waveforms of speed and
currents.
VI.
CONCLUSIONS
This paper has presented the modelling and
experimental result of torque hysteresis controller for
BLDC motor. Torque hysteresis controller has been
applied to a BLDC drive and the results shows that the
current ripple stays within the hysteresis band as defined
by the controller.
ACKNOWLEDGMENT
The authors would like to thank the Universiti Teknikal
Malaysia Melaka (UTeM) for providing the grant for this
research.
73
Lefley, P., L. Petkovska, and G. Cvetkovski. Optimization of
the design parameters of an asymmetric brushless DC motor
for cogging torque minimization in Power Electronics and
Applications (EPE 2011), Proceeding of the 2011-14th
European Conference on 2011.
Hendershot, J.R and T. Miller. Design of Brushless PermanentMagnet Motors. Oxford: Magna Physics Publications &
Oxford Science Publication, 1994.
Ching-Tsai, P. and C. Ting-Yu, An improved hysteresis current
controller for reducing switching frequency. Power Electronics,
IEEE Transactions on, 1994. 9(1): p. 97-104.
KS Low M.F Rahman and K.W Lim. Approaches to the
Control of Torque and Current in Brushless Dc Drive,2002.
Texas Instruments Incorporated. DSP Solutions for BLDC
Motors,1997.
Mayer, J.S. and O. Wasynczuk, Analysis and modelling of a
single-phase brushless DC motor drive system. Energy
Conversion, IEEE Transactions on, 1989. 4(3): p. 473-479.
P.C Sen. Principles of Electric Machine and Power Electronics,
John Wiley,1997. .
Hart, Daniel W. Introduction of Power Electronic, Prentice
hall,2002.
El-Shakawi, A Mohamed. Fundamental of Motor Drives,
Books/Cole Publishing Company,2000.
Anand Sathyan. Digital PWM Control of Brushless Dc Motor
drives, Dec 2008.